Question

1)(4x-1)^2-(5x+2)^2+(8x-7)(8x+7)=28(6-x) 2)(2x-7)^2+(3x-5)^2-2(64-29x)=(4x-9)(9+4x)

Answer 1

1)x1=-2 x2=2 второе не знаю

Answer 2

To solve the given equations, we'll first simplify them and then proceed to find the values of 'x' that satisfy the equations.

1. (4x-1)^2 - (5x+2)^2 + (8x-7)(8x+7) = 28(6-x)

Let's simplify the left side of the equation:

(4x-1)^2 - (5x+2)^2 + (8x-7)(8x+7) = 28(6-x)

Expand and simplify each term:

(16x^2 - 8x + 1) - (25x^2 + 20x + 4) + (64x^2 - 49) = 28(6-x)

Now, combine like terms:

16x^2 - 8x + 1 - 25x^2 - 20x - 4 + 64x^2 - 49 = 28(6-x)

Combine the x^2, x, and constant terms:

(16x^2 - 25x^2 + 64x^2) + (-8x - 20x) + (1 - 4 - 49) = 28(6-x)

55x^2 - 28x - 52 = 28(6-x)

Now, distribute the 28 on the right side:

55x^2 - 28x - 52 = 168 - 28x

Move all terms to one side of the equation:

55x^2 - 28x - 28x - 52 - 168 = 0

Combine like terms:

55x^2 - 56x - 220 = 0

Now, we have a quadratic equation. Let's solve it using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 55, b = -56, and c = -220.

x = (-(-56) ± √((-56)² - 4 * 55 * (-220))) / (2 * 55)

x = (56 ± √(3136 + 48400)) / 110

x = (56 ± √51536) / 110

x = (56 ± 227) / 110

Now, we have two possible solutions:

1. x = (56 + 227) / 110 = 283 / 110
2. x = (56 - 227) / 110 = -171 / 110

So, the solutions to the first equation are x = 283/110 and x = -171/110.

2. (2x-7)^2 + (3x-5)^2 - 2(64-29x) = (4x-9)(9+4x)

Let's simplify the left side of the equation:

(2x-7)^2 + (3x-5)^2 - 2(64-29x) = (4x-9)(9+4x)

Expand and simplify each term:

(4x^2 - 28x + 49) + (9x^2 - 30x + 25) - 2(64-29x) = (4x^2 - 9)(9+4x)

Combine like terms:

4x^2 + 9x^2 - 28x - 30x + 49 + 25 - 2(64-29x) = 4x^2 - 9

Combine like terms on both sides:

13x^2 - 58x + 74 - 2(64-29x) = 4x^2 - 9

Now, distribute the -2 on the left side:

13x^2 - 58x + 74 - 128 + 58x = 4x^2 - 9

Combine like terms:

13x^2 - 54 = 4x^2 - 9

Move all terms to one side of the equation:

13x^2 - 4x^2 - 54 + 9 = 0

Combine like terms:

9x^2 - 45 = 0

Now, divide both sides by 9 to isolate x^2:

x^2 - 5 = 0

Now, add 5 to both sides:

x^2 = 5

Take the square root of both sides (remembering both positive and negative roots):

x = ±√5

So, the solutions to the second equation are x = √5 and x = -√5.